## Introduction: How to Subtract

**Subraction** is the next logical extension of addition and yet causes confusion in students both young and old. Why? We were taught to solve subtraction problems in a confusing way.

I am going to show you a very simple way to subtract large (multi-digit) numbers. You will wonder why they never taught this method in school.

First we need to set some reference points so you can follow along with the concept.

## Step 1: Subtraction, Why the Confusion?

**Subtraction, Why the Confusion**

First - Forget what you were taught, subtraction is really a myth. Addition is where it is at.

Next - I am going to assume you already know a little bit about basic arithmatic, because you are already on the Internet and so can read. I will also assume you know what happens when you had 5 pennies and you lost 2 of those pennies.

KISS, Keep It Simple Silly and don't make subtraction hard on youself.

Each example uses only one of each digit, so you will know exactly which digit is referred to.

In text, each digit from an example will be referred to within square brackets [0], other numbers will be without them.

Terms such as minuend (a) - subtrahend (b) = difference (c) are odd words used to identify and denote parts of the subtraction. Now I do not care if you call them 'one' number, without 'the next' number leaves the "answer'. Just that we both know which is which when I mention them.

## Step 2: Review of Some Basics

According to Wikipedia - Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with. Wow! Now that that is clear.

In mathematical expression, subtraction is denoted by a minus sign in infix notation (a complicated way of saying equation all written on one line). Hmmm, not much better.

The traditional names for the parts of the formula

a - b = c

Where the minuend (a) - subtrahend (b) = difference (c).

## Step 3: Subtract – the American Method

The way most North American students are taught to solve this problem is to think something like this:*Take away [8] from [5] - Oh wait, you can't because [5] is less than [8] so we need to borrow 1 from the tens column, and remember that for later - now take away [8] from 15 which leaves 7 - Ok, then take [2] away from [9] - I mean 8, because we borrowed the 1 from the tens column, remember - So then take away [2] from 8 to leave 6 - The answer should be 67 - Right??.*

Sound familiar, sure it does. Talk about a confusion of thinking with some error prone parts to mess up, like the borrowing and remembering you borrowed etc, Plus the difficulty of learning the concept. It is a wonder any of us managed to program out minds to think like that.

## Step 4: Don’t Subtract Add – the Austrian Method

Try to follow the Austrian or Additions Method thought process of the same example.

What do you need to add to [8] to equal 15 (because [8] is bigger than [5] we make it 15, answer is 7 - now only because we made [5] be 15, add 1 to the [2] giving you 3 - now what do you need to add to 3 to get [9], that would be 6 - so the answer is definitely 67.

Notice the elimination of borrowing from the tens column to remember, and instead carry over and add the 1 to the subtrahend digit in the next column. The carrying is easier than borrowing and remembering. This simple idea clears the most common error in subtracting.

Important to note the Addition Method is so simple that Europeans are taught this method solve difficult multi-digit subtractions in their head.

## Step 5: Proof It to Yourself

If you are one of those, like me, who need to **see it to believe it**. Try this test.

Without aid of pencil and paper - Do this equation both ways.

Hint, you need to have the same answer!

## Step 6: Test Answers

Of course it was easier to use the Austrian Method. Were you even able to do the American Method in your head?

Test your friends. Challange them to see who can subtract large numbers in their head.

Did you get 17268 as the answer??

## Step 7: Subtracting a Bigger Number From a Smaller

Oh, one last point of interest is when you need to subtract a larger number from a smaller one.

Using either Method, make the larger number the minuend and the smaller one the subtrahend proceed as you would to solve for the difference and then just place a "-" sign in front of your answer. How neat is that.

First Prize in the

Burning Questions Round 6.5

Participated in the

Burning Questions Round 6.5

## 15 Discussions

1 year ago

I'd have to spend some time converting my brain over to see if I think it's superior to our familiar method. I suspect the writer is not being totally forthcoming. You still have to borrow when the upper digit is not big enough, but now you have diddling with the bottom digits as well. His example seems pretty impressive, but note that it has "borrowing" in every place (except the last, i.e. left-most). So it gives the impression that you just go down the line, bumping up bottom digits by 1. But in general, you will have to be on your toes, whether or not to boost a bottom digit by 1, and I suspect it might be tougher making decisions top and bottom, rather than the familiar way which just requires a decision on the upper digit.

Regarding that horrible mutilation of the upper digits, it's totally unnecessary. You will know if you just borrowed, the upper digit in the next place chunks down by 1 - no need for scribbling. See http://donaldsauter.com/how-to-subtract.htm

3 years ago

I learned the Austrian Method of adding to subtract at my private Carden school. I taught my children this same easy way and was chastised by their teacher for not following Common Core. Well, F Common Core. Its stupid and ridiculously hard for lrarning minds that young. I say this as a liberal, too. Dont have to be a conservative to know when something doesnt work. That being said, just lose Common Core and give the curriculum back to the individual states and districts. Want to teach your kid creationism, fine, deal with the consequences of your child's science illiteracy.

4 years ago

I know how to do this one,but any other ways?

4 years ago

Wow thank you... Best method ever. Now i can do fast subtraction.

5 years ago on Step 7

wowwwwwwww this is an amazing method thanks alot

7 years ago on Step 7

this is aaaaaaawwwwwwwweeeeeeesssssssooooooommmmmmmeeeeeee it saved my life if there was not this thing i would die by my teacher!!!!!!!!!!!!!!!!!!!!!!!!!!

9 years ago on Step 7

Everyone out. I have to poop. This is amazing. Why were we not taught this method?

Reply 9 years ago on Step 7

Mostly because of a conspiracy from teachers to stretch the little we need to learn into decades of boring classrooms. LOL

North American teaching methods believe the system they taught us is far superior to this European technique. Like-wise with whole word language learning. Don't get me started. LOL

9 years ago on Introduction

ouch, small typo, um that 29,500 should read 28,500

9 years ago on Introduction

okay can you help me with subracting 30,000-1,500 i keep getting 38,500 how do you get the 2 in instead of 3. so when you subtract it is left to right or still right to left??

Reply 9 years ago on Introduction

Sure, I can help. (without rereading my instructable, sorta like one hand behind my back.LOL)

Your example has 6 zeros and the answer has a few too, so it can get real messy real fast describing it, so I'll do each thought process step by step. You will get the aha! moment along the way.

30,000

- 1,500

| | | | |__ think "0 plus 0 gives 0"

| | | |_____ think "0 plus 0 gives 0"

| | |________think "5 plus 5 gives 10" carry forward the 1

| |___________think "1 plus the carried 1 plus 8 gives 10" carry forward the 1

|______________think "the carried 1 plus 2 gives 3"

= 29,500

Working right to left.

It becomes a much more valuable technique the more different the digits are. With so many zero's it is easier to do it other ways, I'll admit.

Now try it with 34,567 - 8,629 and it becomes just as simple as the above.

it quickly becomes

9 + (8) is 17

1 + 2 + (3) is 6

6 + (9) is 15

1 + 8 + (5) is 14

1+(2) is 3

* in the brackets are the answer digits right to left, all the 1's (in this example) are due to carrying forward.

Oh, yeah the answer is 25,938 and with practice can easily be done as quick as you could read it. And it never gets more difficult even when the numbers are larger.

If you do have the aha! moment..... go try subtracting your phone number from your friends, forget about the dashes; and to avoid identical area code thing (yeah use all 10 digits) write one of the numbers in reverse; and you may as well use the higher first digit as the top number.

10 years ago on Step 7

10 years ago on Step 7

Amazing! This is so awesome. I tried it and it works so easily and without any effort. I tried to do some really long problems and i didnt even need to write. Thanks. Im gonna forget the American way! LOL

11 years ago on Introduction

Could you please explain to me how I would subtract 2000.00-632.84? I keep coming up with the wrong number. Your help would really be appreciated. Thanks :0)

Reply 10 years ago on Introduction

Sorry for the late reply. Just found your question. 2000.00 -632.84 Always work from right to left..... 4 and 6 makes 10 6 is the right most digit. add the 1 of that ten to bring the 8 to be a 9 9 and 1 makes the next 10 1 is the second from right digit keep the decimals point lined up. add the 1 of that ten to bring the 2 to be a 3 3 and 7 makes the next 10 7 is the third from right digit add the 1 of that ten to bring the 3 to be a 4 4 and 6 makes the next 10 6 is the fourth from right digit add the 1 of ten to bring the 6 to be a 7 7 and 3 makes the next 10 3 is the fifth from right digit add the 1 of ten to bring the 0 to be a 1 1 and 1 makes the 2 1 is the sixth from right digit You're answer should then be 1367.16 While it seems awkward at first, after a few tries you'll see it is just as easy as addition. If you are still having difficulty try email egon-1@rogers.com and I have other ways to teach this. What part of Ontario? Hope that helps;)